Question

Solve the initial-value problem.

(x^{2} + 1)

dy |

dx |

+ 3x(y − 1) = 0,

y(0) = 4

Answer #1

Solve the given initial-value problem. The DE is a Bernoulli
equation.
x2 dy/dx-2xy=5y^4, y(1)=1/2

1)Consider the following initial-value problem.
(x + y)2 dx + (2xy + x2 − 2) dy =
0, y(1) = 1. Let af/ax = (x + y)2 =
x2 + 2xy + y2. Integrate each term of this
partial derivative with respect to x, letting
h(y) be an unknown function in y.
f(x, y) = + h(y)
Solve the given initial-value problem.
2) Solve the given initial-value problem.
(6y + 2t − 3)
dt + (8y + 6t
− 1) dy...

1) Consider the following initial-value problem.
(x + y)2 dx + (2xy + x2 − 2) dy =
0, y(1) = 1
Let af/ax = (x + y)2 = x2 + 2xy +
y2.
Integrate each term of this partial derivative with respect to
x, letting h(y)
be an unknown function in y.
f(x, y) = + h(y)
Find the derivative of h(y).
h′(y) =
Solve the given initial-value problem.
2) Solve the given initial-value problem.
(6y + 2t − 3)
dt...

Solve the 1st order initial value problem:
1+(x/y+cosy)dy/dx=0, y(pi/2)=0

Consider the initial value problem
dy/dx= 6xy2 y(0)=1
a) Solve the initial value problem explicitly
b) Use eulers method with change in x = 0.25 to estimate y(1)
for the initial value problem
c) Use your exact solution in (a) and your approximate answer in
(b) to compute the error in your approximation of y(1)

solve by the integrating facote method the following initial
value problem
dy/dx=y+x, y(0)=0

Solve the DE:
x(y+1)dx + [(y^2+1)csc(3x)]dy=0

1.Solve the following initial value problem
a) dy/dx= y2/(x-3), with y(4)=2
b) (sqrt(x)) dy/dx = ey+sqrt(x), with y(0)= 0
2. Find an expression for nth term of the
sequence
a) {-1, 13/24, -20/120, 27/720, ...}
b) {4/10, 12/7, 36/4, 108, ...}

Solve the following:
(3x^2 - y^2)dx + (xy - x^3y^-1)dy = 0

Consider the differential equation
x2 dy + y ( x + y) dx = 0 with the initial condition
y(1) = 1.
(2a) Determine the type of the differential equation. Explain
why?
(2b) Find the particular solution of the initial value problem.

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